How can I open a circular window in a cylinder?
Start by adding a circle where the window will go.
E then S to extrude then scale the circle giving making a (still flat) window frame.

Add a Shrinkwrap modifier then a Solidify modifier to the window frame.  Set the Shrinkwrap modifier Target to your main cylinder object. Set the Mode to Project and choose the correct axis for your object (in my example it is the positive Y).
The Solidify modifier is simple, give your window frame the Thickness you want, and set the Offset to 1.

Last step is to cut a circular hole in your mesh for the window. You can do that with a boolean modifier, knife project (how I do it in the gif), or manually adding loop cuts and deleting faces to make a hole. The answers to this question do a good job of explaining the processes.


Animated gif of the entire process.